深圳大学学报理工版

针对磁共振图像(magnetic resonance imaging, MRI)重建质量的问题,提出一种基于加权双层Bregman字典学习方法和图结构正则化稀疏表示的新算法.该算法中,迭代重加权最小l1和图结构正则化稀疏表示模型是被合并到双层Bregman字典学习方法中.加权双层Breman的字典学习方法在外层迭代中增强K空间抽样数据的约束性,在内层迭代中解决Lp的优化.而图结构正则化稀疏表示方法具备捕获图像结构细节的能力,所以从较高的欠采样数据中能完成精确重建.此外,在内层迭代中,重加权最小l1和图结构正则化稀疏表示使算法能快速地趋于收敛.实验结果表明,所提出的算法可有效恢复MRI图像,其峰值信噪比和高频错误的值都优于基于压缩感知的字典学习方法和基于双层Bregman的自适应字典学习方法.

To improve the quality of magnetic resonance imaging, we propose a new dictionary learning algorithm integrating the weighted two-level Bregman and graph regularized sparse coding. We incorporate the iteratively reweighted l1-minimization and graph regularized sparse coding model into the two-level Bregman method with dictionary updating(TBMDU). The weighted two-level Bregman iterative procedure enforces the constraints of K-space sampled data in the outer-level and solves Lp-optimization in the inner-level. The graph regularized sparse coding model has great capacity in capturing structural details of images and, consequently, enables accurate reconstruction from highly under-sampled data. Furthermore, the proposed algorithm is able to converge with a relatively small number of iterations due to the reweighted l1-minimization iteration and graph regularized sparse coding applied in the inner minimization. Simulation results demonstrate that the proposed algorithm can reconstruct MRI images efficiently and outperforms some current approaches, such as dictionary learning for compressed sensing and two-level Bregman method with dictionary updating, in terms of the peak signal-to-noise ratio and the norm value of high-frequency error.

引言
1 理论研究
2 WTBMGR方法
3 实验数据分析与处理
4 结语

图1 在相同二维随机采样轨迹和不同采样因子下的结果<br/>Fig.1 Reconstruction results under the same 2D random sampling and different undersampling factors

图1 在相同二维随机采样轨迹和不同采样因子下的结果
Fig.1 Reconstruction results under the same 2D random sampling and different undersampling factors

图2 在相同采样因子7.14和相同二维随机采样轨迹下,添加混合高斯白噪声的结果<br/>Fig.2 Reconstruction results for the same 7.14-fold undersampling and 2D random sampling under different levels of complex white Gaussian noise added

图2 在相同采样因子7.14和相同二维随机采样轨迹下,添加混合高斯白噪声的结果
Fig.2 Reconstruction results for the same 7.14-fold undersampling and 2D random sampling under different levels of complex white Gaussian noise added

图3 在相同采样因子7.14和不同采样轨迹下的成像结果<br/>Fig.3 Reconstruction results under the 7.14-fold undersampling and different sampling trajectories

图3 在相同采样因子7.14和不同采样轨迹下的成像结果
Fig.3 Reconstruction results under the 7.14-fold undersampling and different sampling trajectories

表1 在相同采样因子7.14和不同采样轨迹下的峰值信噪比<br/>Table 1 The PSNR of the three methods under the same 7.14-fold undersampling and different sampling trajectories

表1 在相同采样因子7.14和不同采样轨迹下的峰值信噪比
Table 1 The PSNR of the three methods under the same 7.14-fold undersampling and different sampling trajectories

图4 在相同采样因子为5和笛卡尔采样轨迹下的复数实验<br/>Fig.4 The complex-valued data under the same 5-fold undersampling and the same Cartesian sampling trajectory

图4 在相同采样因子为5和笛卡尔采样轨迹下的复数实验
Fig.4 The complex-valued data under the same 5-fold undersampling and the same Cartesian sampling trajectory

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备注

引言

1 理论研究

2 WTBMGR方法

3 实验数据分析与处理

4 结语

期刊信息

备注

引言

1 理论研究

2 WTBMGR方法

3 实验数据分析与处理

4 结 语

期刊信息

4 结语